Subgroups — #184355

Order 512.

743 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#443	C₂	1	1	yes	maximal, characteristic
2	#17868	C₂	1	1	yes	maximal, characteristic
3	#17863	C₂	1	1	yes	maximal, characteristic
4	#17337	C₂	1	1	yes	maximal, characteristic, complemented
5	#17320	C₂	1	1	yes	maximal, characteristic, complemented
6	#8297	C₂	1	1	yes	maximal, characteristic, complemented
7	#8296	C₂	1	1	yes	maximal, characteristic, complemented
8	#8267	C₂	1	1	yes	maximal, characteristic, complemented
9	#8194	C₂	1	1	yes	maximal, characteristic, complemented
10	#8194	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#104	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#104	C₂	1	1	yes	maximal, characteristic, complemented
13	#8186	C₂	1	1	yes	maximal, characteristic, complemented
14	#8186	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#322	C₂	1	1	yes	maximal, characteristic, complemented
16	#2965	C₂²	1	1	yes	characteristic
17	#2965	C₂²	1	1	yes	characteristic
18	C₈×#41	C₂²	1	1	yes	characteristic
19	C₈×#41	C₂²	1	1	yes	characteristic
20	C₂×#443	C₄	1	2	yes	—
21	C₄×#135	C₂²	1	1	yes	characteristic
22	C₄×#131	C₂²	1	1	yes	characteristic
23	C₄×#131	C₂²	1	1	yes	characteristic
24	C₄×#108	C₂²	1	1	yes	characteristic
25	#1772	C₄	1	2	yes	—
26	#1764	C₄	1	2	yes	—
27	#1764	C₄	1	2	yes	—
28	C₄×#104	C₂²	1	1	yes	characteristic
29	C₄×#104	C₂²	1	1	yes	characteristic
30	C₄²×C₈	C₂²	1	1	yes	characteristic
31	C₄²×C₈	C₂²	1	1	yes	characteristic
32	C₄²×C₈	C₂²	1	1	yes	characteristic
33	#1588	C₄	1	2	yes	complemented
34	#1587	C₄	1	2	yes	complemented
35	#1586	C₄	1	2	yes	complemented
36	#1585	C₄	1	2	yes	complemented
37	#1584	C₄	1	2	yes	complemented
38	#1583	C₄	1	2	yes	complemented
39	#1582	C₄	1	2	yes	complemented
40	#1581	C₄	1	2	yes	complemented
41	#1564	C₂²	1	1	yes	characteristic
42	#1564	C₂²	1	1	yes	characteristic
43	#1476	C₂²	1	1	yes	characteristic
44	#1476	C₂²	1	1	yes	characteristic
45	#1476	C₂²	1	1	yes	characteristic
46	#1476	C₂²	1	1	yes	characteristic
47	#1455	—	2	1	no	—
48	#1453	—	2	1	no	—
49	#1452	—	2	1	no	—
50	#1452	C₂²	1	1	yes	characteristic
51	#1452	C₂²	1	1	yes	characteristic
52	#1451	—	2	1	no	—
53	#1451	—	2	1	no	—
54	#1451	—	2	1	no	—
55	#1451	C₂²	1	1	yes	characteristic
56	#1451	C₂²	1	1	yes	characteristic
57	C₈×M₁₆	—	2	1	no	—
58	C₈×M₁₆	C₂²	1	1	yes	characteristic
59	C₈×M₁₆	C₂²	1	1	yes	characteristic
60	C₂×#322	—	2	1	no	—
61	C₂×#322	C₂²	1	1	yes	characteristic
62	C₂×#322	C₂²	1	1	yes	characteristic
63	C₂×#322	C₂²	1	1	yes	characteristic
64	C₂×#322	C₂²	1	1	yes	characteristic
65	#1278	C₂²	1	1	yes	characteristic
66	#1278	C₂²	1	1	yes	characteristic
67	#1278	C₂²	1	1	yes	characteristic
68	#1278	C₂²	1	1	yes	characteristic
69	#1276	C₂²	1	1	yes	characteristic
70	#1276	C₂²	1	1	yes	characteristic
71	C₂×#135	C₂×C₄	1	1	yes	characteristic
72	C₂×#131	C₂×C₄	1	2	yes	—
73	C₂×#131	C₂×C₄	1	2	yes	—
74	C₄×#41	C₂³	1	1	yes	characteristic
75	C₄×#41	C₂³	1	1	yes	characteristic
76	#446	C₂×C₄	1	2	yes	—
77	#446	C₂×C₄	1	2	yes	—
78	C₈×Q₈	C₂×C₄	1	2	yes	—
79	C₈×Q₈	C₂×C₄	1	2	yes	—
80	#443	—	2	8	no	—
81	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
82	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
83	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
84	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
85	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
86	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
87	C₄×D₈	C₂×C₄	1	1	yes	characteristic
88	C₄×D₈	C₂×C₄	1	1	yes	characteristic
89	#436	C₂×C₄	1	2	yes	—
90	#436	C₂×C₄	1	2	yes	—
91	#435	—	2	2	no	—
92	#435	—	2	2	no	—
93	C₈×D₄	—	2	2	no	—
94	C₈×D₄	—	2	2	no	—
95	C₈×D₄	C₂×C₄	1	2	yes	—
96	C₈×D₄	C₂×C₄	1	2	yes	—
97	#431	—	2	1	no	—
98	#431	—	2	1	no	—
99	#431	—	2	1	no	—
100	#431	—	2	1	no	—
101	#431	C₂³	1	1	yes	characteristic
102	#431	C₂³	1	1	yes	characteristic
103	#431	C₂³	1	1	yes	characteristic
104	#431	C₂³	1	1	yes	characteristic
105	C₂×#108	C₂×C₄	1	2	yes	—
106	#427	C₂×C₄	1	1	yes	characteristic
107	C₂×#104	C₂×C₄	1	2	yes	—
108	C₂×#104	C₂×C₄	1	2	yes	—
109	#416	C₂×C₄	1	1	yes	characteristic
110	#416	C₂×C₄	1	1	yes	characteristic
111	#405	—	2	2	no	—
112	#405	—	2	2	no	—
113	#405	C₂×C₄	1	2	yes	—
114	#405	C₂×C₄	1	2	yes	—
115	C₄×M₁₆	—	2	1	no	—
116	C₄×M₁₆	—	2	1	no	—
117	C₄×M₁₆	—	2	1	no	—
118	C₄×M₁₆	—	2	1	no	—
119	C₄×M₁₆	C₂³	1	1	yes	characteristic
120	C₄×M₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₄×C₈	—	2	2	no	—
122	C₂×C₄×C₈	—	2	1	no	—
123	C₂×C₄×C₈	—	2	1	no	—
124	C₂×C₄×C₈	—	2	1	no	—
125	C₂×C₄×C₈	—	2	1	no	—
126	C₂×C₄×C₈	—	2	2	no	—
127	C₂×C₄×C₈	C₂×C₄	1	2	yes	—
128	C₂×C₄×C₈	C₂×C₄	1	2	yes	—
129	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
130	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
131	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
132	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
133	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
134	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
135	C₄³	C₂³	1	1	yes	characteristic
136	#341	C₂×C₄	1	2	yes	—
137	#339	C₂×C₄	1	2	yes	—
138	#339	C₂×C₄	1	2	yes	—
139	#335	C₂×C₄	1	2	yes	—
140	#335	C₂×C₄	1	2	yes	—
141	#334	C₂×C₄	1	2	yes	—
142	#334	C₂×C₄	1	2	yes	—
143	Q₈⋊C₈	C₂×C₄	1	2	yes	—
144	Q₈⋊C₈	C₂×C₄	1	2	yes	—
145	Q₈⋊C₈	C₂×C₄	1	2	yes	—
146	Q₈⋊C₈	C₂×C₄	1	2	yes	—
147	D₄⋊C₈	C₂×C₄	1	2	yes	—
148	D₄⋊C₈	C₂×C₄	1	2	yes	—
149	D₄⋊C₈	C₂×C₄	1	2	yes	—
150	D₄⋊C₈	C₂×C₄	1	2	yes	—
151	#322	—	2	1	no	—
152	#322	—	2	1	no	—
153	#322	—	2	1	no	—
154	#322	—	2	1	no	—
155	#322	—	2	1	no	—
156	#322	—	2	1	no	—
157	#322	—	2	1	no	—
158	#322	—	2	1	no	—
159	#322	—	2	1	no	—
160	#322	—	2	1	no	—
161	#322	—	2	2	no	—
162	#322	C₂×C₄	1	2	yes	—
163	#322	C₂×C₄	1	2	yes	—
164	#322	C₂×C₄	1	2	yes	—
165	#322	C₂×C₄	1	2	yes	—
166	#322	D₄	1	1	yes	characteristic
167	#322	D₄	1	1	yes	characteristic
168	#322	D₄	1	1	yes	characteristic
169	#322	D₄	1	1	yes	characteristic
170	C₈²	—	2	1	no	—
171	C₈²	—	2	1	no	—
172	C₂×#41	C₂²×C₄	1	1	yes	characteristic
173	C₂×#41	C₂²×C₄	1	1	yes	characteristic
174	#135	—	2	4	no	—
175	C₂×Q₁₆	C₄²	1	1	yes	characteristic
176	C₂×SD₁₆	C₄²	1	1	yes	characteristic
177	C₂×SD₁₆	C₄²	1	1	yes	characteristic
178	C₂×D₈	C₄²	1	1	yes	characteristic
179	#131	—	2	4	no	—
180	#131	—	2	4	no	—
181	#131	—	4	2	no	—
182	#131	—	4	2	no	—
183	C₂×M₁₆	—	2	2	no	—
184	C₂×M₁₆	—	2	2	no	—
185	C₂×M₁₆	—	2	2	no	—
186	C₂×M₁₆	—	2	2	no	—
187	C₂×M₁₆	C₂²×C₄	1	2	yes	—
188	C₂×M₁₆	C₂²×C₄	1	2	yes	—
189	C₂²×C₈	—	2	1	no	—
190	C₂²×C₈	—	2	1	no	—
191	C₂²×C₈	—	2	2	no	—
192	C₂²×C₈	—	2	2	no	—
193	C₂²×C₈	—	2	2	no	—
194	C₂²×C₈	—	2	2	no	—
195	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₈	C₂²×C₄	1	2	yes	—
198	C₂²×C₈	#41	1	2	yes	—
199	C₂²×C₈	#41	1	2	yes	—
200	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
201	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
202	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
203	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
204	C₄×D₄	—	2	1	no	—
205	C₄×D₄	—	2	1	no	—
206	C₄×D₄	—	2	1	no	—
207	C₄×D₄	—	2	1	no	—
208	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
209	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
210	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
211	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
212	#117	—	2	1	no	—
213	#117	—	2	1	no	—
214	#117	C₂²×C₄	1	1	yes	characteristic
215	#117	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₄²	—	2	1	no	—
217	C₂×C₄²	—	2	1	no	—
218	C₂×C₄²	—	2	1	no	—
219	C₂×C₄²	—	2	1	no	—
220	C₂×C₄²	C₂²×C₄	1	2	yes	—
221	C₂×C₄²	C₂⁴	1	1	yes	characteristic
222	#108	—	2	4	no	—
223	#107	C₄²	1	1	yes	characteristic
224	#107	C₄²	1	1	yes	characteristic
225	#106	C₄²	1	1	yes	characteristic
226	#106	C₄²	1	1	yes	characteristic
227	C₄⋊C₈	—	2	2	no	—
228	C₄⋊C₈	—	2	2	no	—
229	C₄⋊C₈	—	2	2	no	—
230	C₄⋊C₈	—	2	2	no	—
231	C₄⋊C₈	C₂²×C₄	1	2	yes	—
232	C₄⋊C₈	C₂²×C₄	1	2	yes	—
233	C₄⋊C₈	C₂²×C₄	1	2	yes	—
234	C₄⋊C₈	C₂²×C₄	1	2	yes	—
235	#104	—	2	4	no	—
236	#104	M₁₆	1	8	yes	complemented
237	#103	C₄²	1	1	yes	characteristic
238	#103	C₄²	1	1	yes	characteristic
239	#103	C₄²	1	1	yes	characteristic
240	#103	C₄²	1	1	yes	characteristic
241	#102	C₄²	1	1	yes	characteristic
242	#102	C₄²	1	1	yes	characteristic
243	#102	C₄²	1	1	yes	characteristic
244	#102	C₄²	1	1	yes	characteristic
245	C₂²⋊C₈	—	2	1	no	—
246	C₂²⋊C₈	—	2	1	no	—
247	C₂²⋊C₈	—	2	1	no	—
248	C₂²⋊C₈	—	2	1	no	—
249	C₂²⋊C₈	—	2	2	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	—	2	2	no	—
253	#97	—	2	2	no	—
254	#97	—	2	2	no	—
255	#97	—	2	2	no	—
256	#97	—	2	2	no	—
257	#97	—	2	1	no	—
258	#97	—	2	1	no	—
259	C₄×C₈	—	2	8	no	—
260	C₄×C₈	—	2	2	no	—
261	C₄×C₈	—	2	2	no	—
262	C₄×C₈	—	2	2	no	—
263	C₄×C₈	—	2	2	no	—
264	C₄×C₈	—	2	4	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	—	2	1	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	4	2	no	—
274	C₄×C₈	—	4	4	no	—
275	C₄×C₈	C₂²×C₄	1	2	yes	—
276	C₄×C₈	C₂²×C₄	1	2	yes	—
277	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
278	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
279	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
280	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
281	C₄×C₈	C₂²×C₄	1	2	yes	—
282	C₄×C₈	C₂²×C₄	1	2	yes	—
283	C₄×C₈	C₂×D₄	1	1	yes	characteristic
284	C₄×C₈	C₂×D₄	1	1	yes	characteristic
285	C₄×C₈	C₂×D₄	1	1	yes	characteristic
286	C₄×C₈	C₂×D₄	1	1	yes	characteristic
287	C₄×C₈	C₂×D₄	1	1	yes	characteristic
288	C₄×C₈	C₂×D₄	1	1	yes	characteristic
289	C₄×C₈	#41	1	2	yes	—
290	#41	—	2	2	no	—
291	#41	—	2	2	no	—
292	#41	—	2	2	no	—
293	#41	C₂×M₁₆	1	4	yes	—
294	C₂×Q₈	C₂×C₄²	1	1	yes	characteristic
295	C₂×Q₈	C₂×C₄²	1	1	yes	characteristic
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	C₂×C₄²	1	1	yes	characteristic
299	C₂×D₄	C₂×C₄²	1	1	yes	characteristic
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×#41	1	1	yes	characteristic
309	C₂²×C₄	C₂×#41	1	1	yes	characteristic
310	Q₁₆	—	2	2	no	—
311	SD₁₆	—	2	2	no	—
312	SD₁₆	—	2	2	no	—
313	D₈	—	2	2	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	4	4	no	—
318	M₁₆	—	4	4	no	—
319	M₁₆	—	4	4	no	—
320	M₁₆	—	8	2	no	—
321	M₁₆	C₂×M₁₆	1	4	yes	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	4	4	no	—
338	C₂×C₈	—	4	4	no	—
339	C₂×C₈	—	4	2	no	—
340	C₂×C₈	—	4	4	no	—
341	C₂×C₈	—	8	2	no	—
342	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
343	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
344	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
345	C₂×C₈	C₂×C₄²	1	1	yes	characteristic
346	C₂×C₈	C₄×D₄	1	2	yes	—
347	C₂×C₈	C₄×D₄	1	2	yes	—
348	C₂×C₈	C₄×D₄	1	2	yes	—
349	C₂×C₈	C₄×D₄	1	2	yes	—
350	C₂×C₈	C₄×D₄	1	2	yes	—
351	C₂×C₈	C₄×D₄	1	2	yes	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	C₂×C₄²	1	1	yes	characteristic
357	C₄⋊C₄	C₂×C₄²	1	1	yes	characteristic
358	C₄⋊C₄	C₂×C₄²	1	1	yes	characteristic
359	C₄⋊C₄	C₂×C₄²	1	1	yes	characteristic
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	4	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	2	no	—
375	C₄²	C₂×M₁₆	1	4	yes	—
376	C₄²	C₂³×C₄	1	1	yes	characteristic
377	C₄²	C₂³×C₄	1	1	yes	characteristic
378	C₄²	C₂²×D₄	1	1	yes	characteristic
379	C₄²	C₂×#41	1	1	yes	characteristic
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	C₄×#41	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	C₄×M₁₆	1	2	yes	—
387	D₄	—	2	4	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	1	no	—
390	D₄	—	2	1	no	—
391	D₄	—	4	2	no	—
392	D₄	C₄×M₁₆	1	2	yes	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	C₂²×C₄²	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
414	C₂×C₄	C₄×#41	1	1	yes	characteristic
415	C₂×C₄	C₄×#41	1	1	yes	characteristic
416	C₂×C₄	C₂²×M₁₆	1	2	yes	—
417	C₂×C₄	#568	1	2	yes	—
418	C₈	—	2	4	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	2	2	no	—
424	C₈	—	2	2	no	—
425	C₈	—	2	4	no	—
426	C₈	—	2	2	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	2	no	—
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₈	—	4	2	no	—
432	C₈	—	4	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₈	#443	1	4	yes	complemented
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	C₄²×D₄	1	1	yes	characteristic
445	C₂²	#2970	1	2	yes	—
446	C₄	—	2	8	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	1	no	—
455	C₄	C₂×C₄×M₁₆	1	1	yes	characteristic
456	C₄	#2875	1	1	yes	characteristic
457	C₄	D₄×M₁₆	1	2	yes	—
458	C₄	C₂×#443	1	2	yes	—
459	C₄	#2956	1	2	yes	—
460	C₂	—	2	2	no	—
461	C₂	—	4	2	no	—
462	C₂	—	8	1	no	—
463	C₂	#20491	1	1	yes	characteristic
464	C₂	C₄×#443	1	1	yes	characteristic
465	C₂	#20512	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×D₄
commutator	C₂×C₄	C₂²×C₄²
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂²	C₄²×D₄
prime radical	C₂×#135	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄² ◁ C₂×#322 ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #17337	C₂	semidirect
5. #17320	C₂	semidirect
6. #8297	C₂	semidirect
7. #8296	C₂	semidirect
8. #8267	C₂	semidirect
9. #8194	C₂	semidirect
10. #8194	C₂	semidirect
11. C₈×#104	C₂	semidirect
12. C₈×#104	C₂	semidirect
13. #8186	C₂	semidirect
14. #8186	C₂	semidirect
15. C₄×#322	C₂	semidirect
33. #1588	C₄	semidirect
34. #1587	C₄	semidirect
35. #1586	C₄	semidirect
36. #1585	C₄	semidirect
37. #1584	C₄	semidirect
38. #1583	C₄	semidirect
39. #1582	C₄	semidirect
40. #1581	C₄	semidirect
236. #104	M₁₆	semidirect
435. C₈	#443	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×#443	2
#17868	2
#17863	2
#17337	2
#17320	2
#8297	2
#8296	2
#8267	2
#8194	2
C₈×#104	2
#8186	2
C₄×#322	2